It has long been known to correct for probe, or transducer, offset and gain errors with linear equations of the form: S=As+B, where "S" is the corrected signal, "s" is the uncorrected signal, and A and B are correction coefficients. It has also been known to correct for offset, gain, and linearity errors with a quadratic equation of the form: S=Cs.sup.2 +Ds+E, where again "S" is the corrected signal, "s" is the raw data signal, and C, D, and E are correction coefficients. It has even been known to correct for offset, gain, linearity, and higher order non-linearities by the use of third order equations: S=Fs.sup.3 +Gs.sup.2 +Hs+I, where again "S" is the corrected signal, "s" is the uncorrected signal, and F, G, H, and I are the correction coefficients.
Such first, second, and third order correction equations, and the coefficients used with them, are fairly successful at reducing overall error in the corrected signal "S", and increasingly so as additional terms of higher order are employed. They are, however, less effective at dealing with "near-zero" errors, particularly when such errors are expressed as a percentage of the measured value. As the measured value approaches zero, any error that remains becomes much larger by comparison with what is being measured.
For example, if the goal is to measure 150 amperes, and the results are subject to an error of +/-1.0 A, the percentage error is only 0.67%. However, if the goal is to measure 50 amps, and the results are subject to an error of +/-0.5 A, the percentage error increases to 1.0%, even though the absolute error is only half as much as it was at 150 A. Further illustrating this problem, if the goal is to measure only 5.0 A, and the absolute error decreases to 0.2 A, the percentage error nonetheless rises to 4%. Thus, it becomes apparent that offset errors, or apparent offset errors, overtake gain and linearity as the source of percentage error as the quantity being measured approaches zero. By "apparent offset" errors, we include those which arise from the "best fit" process by which the calibration coefficients are derived from the errors in uncorrected data.
Typically, electronic measurement instrument vendors must include two components in accuracy specifications, a constant and a percentage of the measurement result. This dictates that guaranteed accuracy is subject to plus or minus errors that are the greater of a constant and a percentage. What is desired is a way to reduce the "near-zero" or "apparent offset" contribution to residual errors after a correction computation has been performed.